4. Consider the detection problem in the notes p.168-171 but with the threshold detector |Y | > γ =⇒ "say signal present" |Y | < γ =⇒ "say signal absent" (a) Find the probability of detection and the probability of false alarm (b) Find the probability of error. (c) Find the limiting values of the probability of error as γ → +[infinity] and γ → −[infinity].

Please see the attached file for the complete answer.

Step-by-step explanation:

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

i pretty sure it is